81/20: Difference between revisions

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| Color name = g15, gu double octave
| Color name = g15, gu double octave
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The ratio of '''81/20''' is the distance between the 81st and 20th [[harmonic]], which can be seen as a [[4/1|double octave]] that is augmented by a syntonic comma ([[81/80]]). This interval spans the size of about 2421.5 cents. It is also the result of stacking 4 [[6/5]]'s and 3 [[5/4]]'s. This suggests that an [[octave stretch]] of half a syntonic comma is a good way to optimise a [[diatonic scale]] for [[Just intonation|pure]] thirds, resulting in whole tones of approximately 193 cents and [[semitone]]s of 122.
The ratio of '''81/20''' is the distance between the 81st and 20th [[harmonic]], which can be seen as a [[4/1|double octave]] that is augmented by a syntonic comma ([[81/80]]). This interval spans the size of about 2421.5 cents. It is also the result of stacking four [[6/5]]'s and three [[5/4]]'s. This suggests that an [[octave stretch]] of half a syntonic comma is a good way to optimise a [[diatonic scale]] for [[just intonation|pure]] thirds, resulting in whole tones of approximately 193 cents and [[semitone (interval region)|semitones]] of 122.
 
[[Category:Octave]]
{{todo|categorize}}

Latest revision as of 17:04, 26 February 2025

Interval information
Ratio 81/20
Factorization 2-2 × 34 × 5-1
Monzo [-2 4 -1
Size in cents 2421.506¢
Name syntonic double octave
Color name g15, gu double octave
FJS name [math]\displaystyle{ \text{P15}_{5} }[/math]
Tenney norm (log2 nd) 10.6618
Weil norm (log2 max(n, d)) 12.6797
Wilson norm (sopfr(nd)) 21
Open this interval in xen-calc

The ratio of 81/20 is the distance between the 81st and 20th harmonic, which can be seen as a double octave that is augmented by a syntonic comma (81/80). This interval spans the size of about 2421.5 cents. It is also the result of stacking four 6/5's and three 5/4's. This suggests that an octave stretch of half a syntonic comma is a good way to optimise a diatonic scale for pure thirds, resulting in whole tones of approximately 193 cents and semitones of 122.